Question

The number of flags with three strips in order, that can be formed using $2$ identical red, $2$ identical blue, $2$ identical white strips is

• A. $24$
• B. $20$
• C. $90$
• D. $8$

Answer 1

The correct option is A $24$

The number of flags with three strips in order, that

can be formed using 2 identical red, 2 identical blue, 2

identical white strips is.

Sol Given three strips of flags in order they are

2 identical red, 2 identical white, 2 identical blue

(i) Total 3 strips are different but we will arrange

then Number of flags = 3! = 6

(ii) Let take 2 strips are identical

Now, we will have 3 options to select color in

that we will have 2 strips and then 2 options

to select color

Arrangements will be divided by 2!

and as two strips are identical

$\Rightarrow$ Number of flags = $3\times 2\times \frac{3!}{2!}=6\times \frac{6}{2}=\frac{36}{2}$

$=18$

$\therefore$ Total number of flags are = $6+18$

$=24$